Linguistically speaking, both nouns ijaba and istijaba mean basically the same, and "al-Mujeeb" has two meanings: One is: the One Who answers the pleas. The other is: the One Who grants what He is pleaded for.

Al-Mujeeb, Allah, responds to the plea of those who plead to Him and helps them, Who favorably answers the supplication of those who supplicate to Him, Who removes the need of those in need and gives them sufficiently. He even gives prior to being asked and accepts even prior to being pleaded. He knows the need of those who are in need before they pray Him, and He since eternity knows all their needs, so He has provided them with means to satisfy all their needs: He creates foods and all types of sustenance for them; He creates the tools and the means to get such tools to the hands of those who need them. Al-Mujeeb responds to the pleas of those who plead to Him. Since time immemorial, He knew in advance what they needed. He goes to the rescue of those who are in dire need of help, and He does not disappoint anyone who pleads to Him.

This theme recurs quite often throughout the Holy Quran. Examples are:
And Noah called upon us, and most excellent are we to answer the prayer. (37:75) So their Lord accepted their prayer: That I will not waste the deed of one who does a good deed among you, whether male or female, each one of you being from the other. (3:195) And Job (Ayyub) cried out to his Lord: Harm has afflicted me, and you are the most Merciful of the merciful. So we responded to him and removed the harm from him, and we gave him his family and the like (number) of them in addition: a mercy from us and a reminder to the worshippers. (21:83-84) or who answers the [prayer of] the distressed one when he calls upon Him and removes the evil, and who will make you successors in the earth? Is there a god with Allah? Little is it that you mind! (27:62) ... you sought aid from your Lord, so He answered you: I will assist you with a thousand of the angels following one another. (8:9) When My servants ask you concerning Me, then surely I am very near; I answer the prayer of the suppliant when he calls on Me. (2:186)
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And your Lord says: Call upon Me, I will answer you; surely those who are too proud to worship me shall soon enter hell abased. (40:60) For those who respond to their Lord there is goodness, and those who do not respond to Him, had they had all that is in the earth and the like thereof with it, they would certainly have offered it for a ransom. (As for) those (latter ones), an evil reckoning shall be theirs, and their abode is hell, and evil, indeed, is the resting-place. (13:18) O you who believe! Answer (the call of) Allah and His Prophet when he invites you to that which gives you life, and be informed that Allah intervenes between man and his heart, and that to Him you shall be gathered. (8:24)

Allah is capable of responding in various ways. When some of His friends are in need of something, He satisfies their need, and He may even make some circumstances deliberately hard for them only to test them and raise their status due to their perseverance, and to their thanking Him during the time of ease as well as the time of hardship.
So when they almost lose hope, He comes to their rescue with beautiful rewards and with indications of His being pleased with them. Allah guarantees for His servant that He will respond favorably to his supplication in the way which He knows to be in his best interest, and at the time He chooses, rather than the time chosen by His servant; so, do not lose hope because of His delay in answering your plea, for such a delay may prove to be better for you. Allah May even opt to grant you better than what you ask Him for; so, plead to Him as one convinced of His favorable response.

The Messenger of Allah used to say, "Plead to Allah, being convinced of His answer to your pleas, and be advised that Allah does not respond to the pleas of one who is inattentive, indifferent." This tradition has been recorded by al-Tirmithi. He has also said, "No Muslim pleads to Allah a plea wherein there is no desire for committing a sin nor the severing of the ties of kinship except that Allah will grant him one of three good rewards: He will either grant him an immediate response, or He may save the rewards for him in the life hereafter, or He may keep its equivalent of evil away from him." His companions said, "Then we will plead to Him a great deal, indeed." He said, "Surely Allah is greater still!"

The Messenger of Allah has said, "When you have a plea, plead to Allah, and whenever you need help, seek help from Allah." In another tradition, he says, "Allah is too shy to disappoint any of His servants who plead to Him for something good."